What to Do When Input Voltage is Variable? | 5-20mA Range Explained

[Kaguro]

Homework Statement

A zener regulator has an input voltage in the range 15V-20V and a load current in the range of 5mA-20mA. If the zener voltage is 6.8V, the value of the series resistor should be:
(a)390Ω
(b)420Ω
(c)440Ω
(d)460Ω

Relevant Equations

Stuff

This is a very confusing situation for me. If the input voltage were constant, then I would be able to understand that by varying load resistance, I can change the current through it, such that the drop across the load = Vz = 6.8V.

But the input voltage is also not constant. So what am I to understand? The 5-20mA range is for what voltage?

I only know:
If Vs is source voltage, then
Vs- I*Rs - 6.8=0
So, I*Rs = Vs-6.8

So, Imax = (20-6.8)/Rs
Imin = (15-6.8)/Rs

This is total current through series resistor. Some of it will run through zener and some through load. But load itself is variable.

Please show me some way.

 

[berkeman]

I think the limiting case is that R has to be small enough to pass at least the required load current when the input voltage is at its minimum. R can be smaller, but that just wastes extra power in the Zener diode. (It's unfortunate that they did not give you a real V-I curve for the Zener, so you could include its Zener current at 6.8V, but whatever).

Using that datapoint, I think you will see that only one of the choices that you are given will work. Can you show the calculation for the case I described?

 

[Kaguro]

So the input voltage is minimum, Vs=15V.

Now R is small enough to allow for the load current to flow. Now that our source is fixed, we can decrease the load resistance so as to accept all the current and leave none for the zener.

So Iz=0 and IL=I
This is limiting case and zener should still drop approximately 6.8V.

Now since we made load small, it should conduct maximum current to have IL=20mA.

Now, 15-IR-6.8=0
And I=20mA.

So we get R= 410 ohm.

Now tell me what's wrong.

 

[berkeman]

Now tell me what's wrong.

Nothing is wrong, that is the same number I calculated. Now remember my comment about how R can be less than that value -- all that does is waste a little power in Iz. So the correct answer out of your multiple choices is...

 

[Kaguro]

Nothing is wrong, that is the same number I calculated. Now remember my comment about how R can be less than that value -- all that does is waste a little power in Iz. So the correct answer out of your multiple choices is...

(A)390 ohm.

Thanks very much!

 

[gneill]

(It's unfortunate that they did not give you a real V-I curve for the Zener, so you could include its Zener current at 6.8V, but whatever)

True. Some textbooks provide an appendix with sample datasheets for typical parts for some of the examples and problems. Might be worth checking.

Now R is small enough to allow for the load current to flow. Now that our source is fixed, we can decrease the load resistance so as to accept all the current and leave none for the zener.

Rough rule of thumb for relatively low voltage / power zeners is to assume a minimum zener on-current of between 5 and 10 mA. Unless the zener is at least turned on and biased to the zener region it won't be providing adequate regulation, and performance will likely be wonky near the lower range of the input voltage.

 

[berkeman]

Rough rule of thumb for relatively low voltage / power zeners is to assume a minimum zener on-current of between 5 and 10 mA. Unless the zener is at least turned on and biased to the zener region it won't be providing adequate regulation, and performance will likely be wonky near the lower range of the input voltage.

Yeah, that's why I really wanted to have a datasheet to check. It's surprising how inefficient Zener regulators are, once you factor in the Iz needed to get Vz into the rated voltage range.

The problem seems to be (over-) simplifying to say that the Vz = 6.8V even without any Iz. At least that's the way I'm interpreting it so far...

 

[DaveE]

It's surprising how inefficient Zener regulators are

Yes. They make for good circuit design teaching. However, in the modern world, you're going to use an IC regulator in any but the simplest clamping applications.